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Simplifying 4p2 + 3p + -18 = 0 Reorder the terms: -18 + 3p + 4p2 = 0 Solving -18 + 3p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 0.75p + p2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.75p + 4.5 + p2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.75p + p2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.75p + p2 = 0 + 4.5 0.75p + p2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.75p + p2 = 4.5 The p term is 0.75p. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75p + 0.140625 + p2 = 4.5 + 0.140625 Reorder the terms: 0.140625 + 0.75p + p2 = 4.5 + 0.140625 Combine like terms: 4.5 + 0.140625 = 4.640625 0.140625 + 0.75p + p2 = 4.640625 Factor a perfect square on the left side: (p + 0.375)(p + 0.375) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (p + 0.375) equal to 2.154210992 and -2.154210992.Subproblem 1
p + 0.375 = 2.154210992 Simplifying p + 0.375 = 2.154210992 Reorder the terms: 0.375 + p = 2.154210992 Solving 0.375 + p = 2.154210992 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + p = 2.154210992 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + p = 2.154210992 + -0.375 p = 2.154210992 + -0.375 Combine like terms: 2.154210992 + -0.375 = 1.779210992 p = 1.779210992 Simplifying p = 1.779210992Subproblem 2
p + 0.375 = -2.154210992 Simplifying p + 0.375 = -2.154210992 Reorder the terms: 0.375 + p = -2.154210992 Solving 0.375 + p = -2.154210992 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + p = -2.154210992 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + p = -2.154210992 + -0.375 p = -2.154210992 + -0.375 Combine like terms: -2.154210992 + -0.375 = -2.529210992 p = -2.529210992 Simplifying p = -2.529210992Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.779210992, -2.529210992}
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